How to calculate the correlation function in twisted SYM \(N=2\), \(N_f=4\) QFT on a projective plane
Let \({\mathfrak M}\) be the moduli space of \(\mu\)-stable torsion-free coherent sheaves \(F\) with \(\text{rk} (F)=2\), \(c_1(F)=-1\), \(c_2(F)=k\) on \(P_2(C)\) and \({\mathcal G}\) the universal bundle on \({\mathfrak M}\). The sequence of the topological constants \(a_k=c_{4k-4} ({\mathcal G}^{\otimes 4})\) appears as coefficients of the correlation function in the \(N=2\), \(N_f=4\) supersymmetric Yang-Mills theory with \(SO(3)\) gauge group [\textit{Ch. Okonek}, \textit{M. Schneider}, and \textit{H. Spindler}, Vector bundles on complex projective spaces, Prog. Math. 3 (1980; Zbl 0438.32016)]. One explains how to calculate the coefficients \(a_k\) for SYM \(N=2\) \(SO(3)\)-gauge QFT with four flavors (spinor fields) in terms of top Chern classes of \({\mathcal G}\), and one calculates several initial coefficients \((k=1,2, \dots,7)\) via the Bott residue formula. A geometrical description of the moduli spaces with 2-dimensional torus action on them is given. See also [\textit{A. L. Gorodentsev}, in ``Algebraic geometry and its applications'', Aspects Math. E 25, 47-59 (1994; Zbl 0845.14011)].
scientific article; zbMATH DE number 1017619
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